A covariant quark model, based both on the spectator formalism and on vector meson dominance, and previously calibrated by the physical data, is here extended to the unphysical region of the lattice data by means of one single extra adjustable parameter - the constituent quark mass in the chiral limit. We calculated the Nucleon (N) and the gamma N -> Delta form factors in the universe of values for that parameter described by quenched lattice QCD. A qualitative description of the Nucleon and gamma N -> Delta form factors lattice data is achieved for light pions.
We show how one may define baryon constituent quarks in a rigorous manner, given physical assumptions that hold in the large-N_c limit of QCD. This constituent picture gives rise to an operator expansion that has been used to study large-N_c baryon observables; here we apply it to the case of charge radii of the N and Delta states, using minimal dynamical assumptions. For example, one finds the relation r_p^2 - r_{Delta^+}^2 = r_n^2 - r_{Delta^0}^2 to be broken only by three-body, O(1/N_c^2) effects for any N_c.
We examine the role of the Delta-Delta intermediate state in low energy NN scattering using effective field theory. Theories both with and without pions are discussed. They are regulated with dimensional regularization and MSbar subtraction. We find that the leading effects of the Delta-Delta state can be absorbed by a redefinition of the contact terms in a theory with nucleons only. It does not remove the requirement of a higher dimension operator to reproduce data out to moderate momentum. The explicit decoupling of the Delta-Delta state is shown for the theory without pions.
We calculate the masses of the nucleons and deltas in twisted mass heavy baryon chiral perturbation theory. We work to quadratic order in a power counting scheme in which we treat the lattice spacing and the quark masses to be of the same order. We give expressions for the mass and the mass splitting of the nucleons and deltas both in and away from the isospin limit. We give an argument using the chiral Lagrangian treatment that, in the strong isospin limit, the nucleons remain degenerate and the delta multiplet breaks into two degenerate pairs to all orders in chiral perturbation theory. We s…
Information on the intrinsic deformation of the proton can be obtained by studying the electromagnetic p-->Delta+ quadrupole transition. Recent experiments have shown that the electric quadrupole (E2) strength in gamma p --> Delta+ is about 10 times larger than predicted by the simple quark model using only one-body currents. Our analysis provides evidence for the dominance of exchange currents in the N-->Delta quadrupole transition and identifies the physical mechanism leading to the observed E2 strength.
In a world with two quark flavors and a large number of colors (N_c), the polarized and unpolarized quark distributions in the delta are completely determined by those in the nucleon up to {\cal O}(1/N_c). In particular, we find q_Δ(x) =[(1\pm 2T_z)u_N(x)+ (1\mp 2T_z)d_N(x)]/2 and Δq_Δ(x) =[(5\pm 2T_z)Δu_N(x) + (5\mp 2T_z)Δd_N(x)]/10, where q = u, d and $T_z$ the charge state of a delta. The result can be used to estimate the leading chiral-logarithmic corrections to the quark distributions in the nucleon.
Strong isospin breaking in the spectrum of the nucleons and deltas can be studied in lattice QCD with the help of chiral perturbation theory. At leading order in the chiral expansion, the mass splittings between the proton and neutron and between the deltas are linear in the quark mass difference. The next-to-leading order contributions to these splittings vanish even away from the strong-isospin limit. Therefore, any non-linear quark mass dependence of these mass splittings is a signal of the next-to-next-to-leading order mass contributions, thus providing access to LECs at this order. We det…
We have evaluated nucleon and pion electromagnetic form factors using for the first time eigenfunctions of a light-front mass operator, reproducing a large set of energy levels, and constituent quark form factors in the one-body current. The comparison with the experimental data yields valuable information on the electromagnetic structure of light constituent quarks and on the different role played by their Dirac and Pauli form factors.
We perform a relativistic chiral effective-field theory calculation of the pion electroproduction off the nucleon ($e^- N \to e^- N π$) in the Delta(1232)-resonance region. After fixing the three low-energy constants, corresponding to the magnetic (M1), electric (E2), and Coulomb (C2) $γNΔ$ couplings, our calculation provides a prediction for the momentum-transfer and pion-mass dependence of the $γNΔ$ form factors. The prediction for the pion-mass dependence resolves the discrepancy between the recent lattice QCD results and the experimental value for the "C2/M1 ratio" at low $Q^2$.
The electromagnetic form factors of the nucleon are calculated in an extended chiral constituent-quark model where the effective interaction is described by the exchange of pseudoscalar, vector, and scalar mesons. Two-body current-density operators, constructed consistently with the extended model Hamiltonian in order to preserve gauge invariance and current conservation, are found to give a significant contribution to the nucleon magnetic form factors and improve the estimates of the nucleon magnetic moments.
Nucleon and pion electromagnetic form factors are evaluated in the spacelike region within a light-front constituent quark model, where eigenfunctions of a mass operator, reproducing a large set of hadron energy levels, are adopted and quark form factors are considered in the one-body current. The hadron form factors are sharply affected by the high momentum tail generated in the wave function by the one-gluon-exchange interaction. Useful information on the electromagnetic structure of light constituent quarks can be obtained from the comparison with nucleon and pion experimental data.
We study the short-range nucleon-nucleon interaction in a chiral constituent quark model by diagonalizing a Hamiltonian comprising a linear confinement and a Goldstone boson exchange interaction between quarks. The six-quark harmonic oscillator basis contains up to two excitation quanta. We show that the highly dominant configuration is $\mid s^4p^2[42]_O [51]_{FS}>$ due to its specific flavour-spin symmetry. Using the Born-Oppenheimer approximation we find a strong effective repulsion at zero separation between nucleons in both $^3S_1$ and $^1S_0$ channels. The symmetry structure of the highl…
We study the N-Delta-gamma transition in the Dyson-Schwinger approach. The nucleon and Delta baryons are treated as quark-diquark bound states, where the ingredients of the electromagnetic transition current are computed self-consistently from the underlying dynamics in QCD. Although our approach does not include pion-cloud effects, we find that the electric and Coulomb quadrupole form-factor ratios R_EM and R_SM show good agreement with experimental data. This implies that the deformation from a spherical charge distribution inside both baryons can be traced back to the appearance of p waves …
The complete spin structure of the pion-nucleon-loop contribution to the delta self-energy and dressed propagator is calculated in vacuum, with the most general form of the pion-nucleon-delta vertex. The imaginary parts of the ten Lorentz-scalar coefficients are calculated in closed form, while the real parts are obtained numerically from a dispersion relation. The effect of the pion-nucleon-delta coupling constants and form-factor on the pion-nucleon phase-shift in the spin-3/2 isospin-3/2 channel is studied.
We study the strong couplings of the nucleon and delta resonances in a collective model. In the ensuing algebraic treatment we derive closed expressions for decay widths which are used to analyze the experimental data for strong decays into the pion and eta channels.
We calculate the nucleon and the delta mass to fourth order in a covariant formulation of the small scale expansion. We analyze lattice data from the MILC collaboration and demonstrate that the available lattice data combined with our knowledge of the physical values for the nucleon and delta masses lead to consistent chiral extrapolation functions for both observables up to fairly large pion masses. This holds in particular for very recent data on the delta mass from the QCDSF collaboration. The resulting pion-nucleon sigma term is sigma_{piN} = 48.9 MeV. This first quantitative analysis of t…
We study the momentum and the quark mass dependence of the axial nucleon to Delta(1232) transition form factors in the framework of non-relativistic chiral effective field theory to leading-one-loop order. The outcome of our analysis provides a theoretical guidance for chiral extrapolations of lattice QCD results with dynamical fermions.
Results for the proton and neutron electric and magnetic form factors as well asthe nucleon axial and induced pseudoscalar form factors are presented for the chiral constituent quark model based on Goldstone-boson-exchange dynamics. The calculations are performed in a covariant framework using the point-form approach to relativistic quantum mechanics. The direct predictions of the model yield a remarkably consistent picture of the electroweak nucleon structure.
We present a coupled system of integral equations for the pi pi --> Nbar N and Kbar K --> Nbar N S-waves derived from Roy-Steiner equations for pion-nucleon scattering. We discuss the solution of the corresponding two-channel Muskhelishvili-Omnes problem and apply the results to a dispersive analysis of the scalar form factor of the nucleon fully including Kbar K intermediate states. In particular, we determine the corrections Delta_sigma and Delta_D, which are needed for the extraction of the pion-nucleon sigma term from pi N scattering, and show that the difference Delta_D - Delta_sigma=(-1.…
We present a model description of the nucleon valence structure function applicable over the entire region of the Bjorken variable x, and above moderate values of Q**2 (> 1 GeV**2). We stress the importance of describing the complete spectrum of intermediate states which are spectator to the deep-inelastic collision. At a scale of 1 GeV**2 the relevant degrees of freedom are constituent quarks and pions. The large-x region is then described in terms of scattering from constituent quarks in the nucleon, while the dressing of constituent quarks by pions plays an important role at intermediate x …
The axial form factor G_A of the nucleon is investigated for the Goldstone-boson-exchange constituent quark model using the point-form approach to relativistic quantum mechanics. The results, being covariant, show large contributions from relativistic boost effects. The predictions are obtained directly from the quark-model wave functions, without any further input such as vertex or constituent-quark form factors, and fall remarkably close to the available experimental data.
We study the chiral behavior of the nucleon and $Δ$-isobar masses within a manifestly covariant chiral effective-field theory, consistent with the analyticity principle. We compute the $πN$ and $πΔ$ one-loop contributions to the mass and field-renormalization constant, and find that they can be described in terms of universal relativistic loop functions, multiplied by appropriate spin, isospin and coupling constants. We show that these relativistic one-loop corrections, when properly renormalized, obey the chiral power-counting and vanish in the chiral limit. The results including only the $πN…
The electromagnetic form factors are the most fundamental quantities to describe the internal structure of the nucleon and the shape of a spatially extended particle is determined by its {\it intrinsic} quadrupole moment which is first order moment of the charge density operator. With some experimental indications of a deformed nucleon, we have calculated the {\it intrinsic} quadrupole moment of the octet and decuplet baryons in the framework of chiral constituent quark model \chiCQM which is quite successful in explaining some of the important baryon properties in the nonperturbative regime.
We study nucleon-to-delta electromagnetic transition form factors and relations between them within the framework of holographic dual model of QCD proposed by Sakai and Sugimoto. In this setup, baryons appear as topological solitons of the five dimensional holographic gauge theory that describes a tower of mesons and their interactions. We find a relativistic extension of the nucleon-delta-vector meson interaction vertices and use these to calculate transition form factors from holographic QCD. We observe that at low momentum transfer, magnetic dipole, electric and Coulomb quadrupole form fact…
We investigate the nucleon to Delta(1232) vector and axial vector amplitudes in the non-relativistic quark model of the Isgur-Karl variety. A particular interest is to investigate the SU(6) symmetry breaking, due to color hyperfine interaction. We compare the theoretical estimates to recent experimental investigation of the Adler amplitudes by neutrino scattering.
A qualitative QCD analysis and a quantitative model calculation are given to show that the constituent quark model remains a good approximation even with the nucleon spin structure revealed in polarized deep inelastic scattering taking into account.
We develop a formally covariant quark-diquark model of the nucleon. The nucleon is treated as a bound state of a constituent quark and a diquark interacting via a quark exchange. We include both scalar and axial-vector diquarks. The underlying Bethe-Salpeter equation is transformed into a pair of coupled Salpeter equations. The space- and timelike electromagnetic form factors of the nucleon are calculated in the Mandelstam formalism for squared momentum transfers up to 3 (GeV/c)^2 above threshold. The model is applied also to the Delta(3/2).
We define a constituent quark within QCD. It is shown that the spin of such a quark and hence also the spin of the nucleon reduced due to $\bar{q}q$-pairs, in agreement with experiment. A solution to the spin problem is given.
A relativistic quark model and a new set of wave functions of nucleon and Delta have been used to study the electromagnetic propertities of (1/2)^+ baryons and photoelectric production of Delta(1236).
Previous extrapolations of lattice QCD results for the nucleon mass to the physically relevant region of small quark masses, using chiral effective field theory, are extended and expanded in several directions. A detailed error analysis is performed. An approach with explicit delta(1232) degrees of freedom is compared to a calculation with only pion and nucleon degrees of freedom. The role of the delta(1232) for the low-energy constants of the latter theory is elucidated. The consistency with the chiral perturbation theory analysis of pion-nucleon scattering data is examined. It is demonstrate…
We examine isospin breaking in the nucleon wave functions due to the $u - d$ quark mass difference and the Coulomb interaction among the quarks, and their consequences on the nucleon electroweak form factors in a nonrelativistic constituent quark model. The mechanically induced isospin breaking in the nucleon wave functions and electroweak form factors are exactly evaluated in this model. We calculate the electromagnetically induced isospin admixtures by using first-order perturbation theory, including the lowest-lying resonance with nucleon quantum numbers but isospin 3/2. We find a small ($\…
Nucleon generalized polarizabilities are investigated within a relativistic framework, defining such quantities through a Lorentz covariant multipole expansion of the amplitude for virtual Compton scattering. The key physical ingredients in the calculation of the nucleon polarizabilities are the Lorentz invariant reduced matrix elements of the electromagnetic transition current, which can be evaluated from off-energy-shell helicity amplitudes. The evolution of the proton paramagnetic polarizability, $β_{para}(q)$, as a function of the virtual-photon three-momentum transfer $ q,$ is explicitly …
Using a covariant spectator constituent quark model we predict an electric quadrupole moment -0.043 efm^2 and a magnetic octupole moment -0.0035 efm^3 for the Delta+ excited state of the nucleon.
We formulate a new power-counting scheme for a chiral effective field theory of nucleons, pions, and Deltas. This extends chiral perturbation theory into the Delta-resonance region. We calculate nucleon Compton scattering up to next-to-leading order in this theory. The resultant description of existing $γ$p cross section data is very good for photon energies up to about 300 MeV. We also find reasonable numbers for the spin-independent polarizabilities $α_p$ and $β_p$.
We investigate the model dependence and the importance of choice of database in extracting the {\it physical} nucleon-Delta(1232) electromagnetic transition amplitudes, of interest to QCD and baryon structure, from the pion photoproduction observables. The model dependence is found to be much smaller than the range of values obtained when different datasets are fitted. In addition, some inconsistencies in the current database are discovered, and their affect on the extracted transition amplitudes is discussed.
The nucleon-nucleon problem is studied as a six-quark system in a nonrelativistic chiral constituent quark model where the Hamiltonian contains a linear confinement and a pseudoscalar meson (Goldstone boson) exchange interaction between the quarks. This hyperfine interaction has a long-range Yukawa-type part, depending on the mass of the exchanged meson and a short-range part, mainly responsible for the good description of the baryon spectra.
Results for all elastic electroweak nucleon form factors are presented for the chiral constituent quark model based on Goldstone-boson-exchange dynamics. The calculations are performed in a covariant framework using the point-form approach to relativistic quantum mechanics. The direct predictions of the model yield a remarkably consistent picture of the electroweak nucleon structure.
We investigate the axial-vector nucleon-to-delta transition form factors in the framework of relativistic baryon chiral perturbation theory at the one-loop order using the complex-mass renormalization scheme. We determine the available six free parameters by fitting to an empirical parametrization of the form factors obtained from the BNL neutrino bubble chamber experiments. A unique feature of our calculation is the prediction of a non-vanishing form factor $C_3^A(Q^2)$. Moreover, our results show a surprising sensitivity to the coupling constant $\texttt{g}_1$ of the leading-order Lagrangian…
The D(03) dibaryon is generated dynamically as a resonance pole in a pion-nucleon-Delta' three-body model, where Delta' is a stable Delta baryon. Using separable interactions dominated by the Delta(1232) isobar for pion-nucleon and by the D(12) isobar for nucleon-Delta', where D(12) is the nucleon-Delta 2150 MeV dibaryon deduced in and constrained by 1D2 pp scattering, the model reduces to an effective two-body problem for Delta-Delta' which is solved. The mass and width of D(03) are found close to those of the I(JP)=0(3+) resonance peak observed by WASA@COSY in pion-production pn collisions a…
N-Delta and Delta-Delta dibaryon candidates are discussed and related quark-based calculations are reviewed. New hadronic calculations of L=0 nonstrange dibaryon candidates are reported. For N-Delta, I(JP)=1(2+) and 2(1+) S-matrix poles slightly below threshold are found by solving pi-N-N Faddeev equations with relativistic kinematics, and for Delta-Delta several S-matrix poles below threshold are found by solving pi-N-Delta Faddeev equations with relativistic kinematics in which the N-Delta interaction is dominated by the 1(2+) and 2(1+) resonating channels. In particular, the I(JP)=0(3+) Del…
The main statement of the nucleon constituent quark model with a fixed number of particles as basic ansatz are considered in a framework of the single-time (quasipotential) approach to the bound state problem. The scaling law breacking for the proton form factor is investigated for Q^2 = 0 -- 2 Gev^2.
The Drell-Hearn-Gerasimov sum rule for the nucleon is investigated within a relativistic constituent quark model formulated on the light-front. The contribution of the N - Delta(1232) transition is explicitly evaluated using different forms for the baryon wave functions and adopting a one-body relativistic current for the constituent quarks. It is shown that the N - Delta(1232) contribution to the sum rule is sharply sensitive to the introduction of anomalous magnetic moments for the constituent quarks, at variance with the findings of non-relativistic and relativized quark models. The experim…
Without any further adjusting of parameters, a relativistic constituent quark model, successful in the description of the data for the nucleon elastic form factors and of the dominant contribution for the nucleon to Delta electromagnetic transition, is used here to predict the dominant electromagnetic form factors of the Delta baryon. The model is based on a simple Delta wave function corresponding to a quark-diquark system in an S-state. The results for E0 and M1 are consistent both with experimental results and lattice calculations. The remaining form factors E2 and M3 vanish, given the symm…
An expansion of the electromagnetic form factors of the nucleon and Delta(1232) in small momentum transfer and pion mass is performed in a manifestly-covariant EFT framework consistent with chiral symmetry and analyticity. We present the expressions for the nucleon and Delta(1232) electromagnetic form factors, charge radii, and electromagnetic moments in the framework of SU(2) baryon chiral perturbation theory, with nucleon and Delta(1232)-isobar degrees of freedom, to next-to-leading order. Motivated by the results for the proton electric radius obtained from the muonic-hydrogen atom and elec…
We present the results of a third order calculation of the pion-nucleon scattering amplitude in a chiral effective field theory with pions, nucleons and delta resonances as explicit degrees of freedom. We work in a manifestly Lorentz invariant formulation of baryon chiral perturbation theory using dimensional regularization and the extended on-mass-shell renormalization scheme. In the delta resonance sector, the on mass-shell renormalization is realized as a complex-mass scheme. By fitting the low-energy constants of the effective Lagrangian to the $S$- and $P$-partial waves a satisfactory des…
We develop a generalized version of heavy-baryon chiral perturbation theory to describe pion-nucleon scattering in a kinematic domain that extends continuously from threshold to the delta-isobar peak. The $P$-wave phase shifts are used to illustrate this framework.
Instanton effects can give large contribution to strong interacting processes, especially at the energy scale where perturbative QCD is no longer valid. However instanton contribution to the gluon contribution in constituent quark and nucleon has never been calculated before. Based on both the constituent quark picture and the instanton model for QCD vacuum, we calculate the unpolarized and polarized gluon distributions in the constituent quark and in the nucleon for the first time. We find that the pion field plays an important role in producing both the unpolarized and the polarized gluon di…
The electromagnetic form factors of the nucleon have been calculated in a chiral constituent-quark model. The nucleon wave functions are obtained by solving a Schrödinger-type equation for a semi-relativistic Hamiltonian with an effective interaction derived from the exchange of mesons belonging to the pseudoscalar octet and singlet and a linear confinement potential. The charge-density current operator has been constructed consistently with the model Hamiltonian in order to preserve gauge invariance and to satisfy the continuity equation.
The spin properties and the flavor asymmetric sea of the nucleon can be well explained by assuming that each constituent quark is surrounded with about 30% probability by a quark-antiquark pair coupled to the pion quantum numbers. We show that about one quarter of these quark-antiquark pairs show up as the pion in $\p\to\nπ^+$ and $\p\to\pπ^0$ fluctuation in agreement with the observed value in the ($\e+\p\to\e+$ forward neutron+X) experiment.
Three-body hadronic models with separable pairwise interactions are formulated and solved to calculate resonance masses and widths of L=0 N-Delta and Delta-Delta dibaryons using relativistic kinematics. For N-Delta, I(JP)=1(2+) and 2(1+) resonances slightly below threshold are found by solving pi-N-N Faddeev equations. For Delta-Delta, several resonances below threshold are found by solving pi-N-Delta Faddeev equations in which the N-Delta interaction is dominated by the 1(2+) and 2(1+) resonating channels. The lowest Delta-Delta dibaryon resonances found are for I(JP)=0(3+) and 3(0+), the for…
We calculate the form factors of the electromagnetic nucleon-to-$Δ$-resonance transition to third chiral order in manifestly Lorentz-invariant chiral effective field theory. For the purpose of generating a systematic power counting, the complex-mass scheme is applied in combination with the small-scale expansion. We fit the results to available empirical data.
The electromagnetic form factors are the most fundamental quantities to describe the internal structure of the nucleon and the shape of a spatially extended particle is determined by its intrinsic quadrupole moment which can be related to the charge radii. We have calculated the electromagnetic form factors, nucleon charge radii and the intrinsic quadrupole moment of the nucleon in the framework of chiral constituent quark model. The results obtained are comparable to the latest experimental studies and also show improvement over some theoretical interpretations.
This thesis constitute an investigation of finding out whether or not the Goldstone Boson Exchange (GBE) model can give rise to a short-range repulsion in the the nucleon-nucleon (NN) interaction. We used two different approaches based on the Born-Oppenheimer approximation and taking into account Harvey's transformations. Next, we study the NN interaction in a dynamical way using the resonating group method (RGM). We present results for the s-wave phase shifts in the NN scattering. We also introduce some necessary extensions of the GBE model like the contribution of the sigma-meson exchange in…
We present a calculation of the polarized rho meson cloud in a nucleon using time-ordered perturbation theory in two different variants advocated in the literature. We calculate the induced difference between the distributions Delta d^bar(x) and Delta u^bar(x). We use a recent lattice calculation to motivate an ansatz for the polarized valence quark distribution of the rho meson. Our calculations show that the two theoretical approaches give vastly different results. We conclude that Delta d^bar(x) - Delta u^bar(x) can be of relevant size with important consequences for the combined fits of po…
We present a model of baryonic matter which contains free constituent quarks in addition to bound constituent quarks in nucleons. In addition to the common linear sigma-model we include the exchange of vector-mesons. The percentage of free quarks increases with baryon density but the nucleons resist a restoration of chiral symmetry.
The first moment of longitudinal and transverse spin densities of quarks in the nucleon are calculated in a light-front constituent quark model for the different cases of quark and nucleon polarization. Significant distortions are found for the transverse spin densities. In particular the Sivers function is predicted with opposite sign for up and down quarks and the Boer-Mulders function is predicted large and negative for both up and down quarks, in agreement with lattice calculations. Quite a different spin distribution is obtained for up and down quarks in the cases of quarks and proton tra…
Influence of the effects of the pion-nucleon and nucleon-nucleon re-scattering on the polarization observables of the reaction gamma + d = p + p + pi- in Delta - isobar region is investigated. Pion-nucleon and nucleon-nucleon re-scattering are studied in the diagrammatic approach. Relativistic-invariant forms of the pion photoproduction and pion-nucleon scattering operators are used. The unitarization procedure in K-matrix approach is applied for the resonance partial amplitudes. It is shown a considerable influence of the re-scattering effects on the polarization observables of this reaction …
A nonrelativistic decomposition for the quark energy by the ratio of the dispersion of quark momentum squared and the effective quark mass is investigated in the framework of the relativistic oscillator constituent quark model as bound systems of three valence quarks. It is shown that relativistic corrections are defined by dispersion of the squared absolute value of the quark momentum. The variations of the quark mass and oscillator parameter are studied in detail both in the spectrum and in the nucleon magnetic moments.
The pretzelosity distribution function $h_{1T}^\perp$ is studied in a covariant the quark-parton model which describes the structure of the nucleon in terms of 3D quark intrinsic motion. This relativistic model framework supports the relation between helicity, transversity and pretzelosity observed in other relativistic models {\sl without} assuming SU(6) spin-flavor symmetry. Numerical results and predictions for SIDIS experiments are presented.
